Invariant means and finite representation theory of C*-algebras

2003/04/01 by Nathanial P. Brown, Brown, Nathanial P. · 16 citations
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.math/0304009

Abstract

Various subsets of the tracial state space of a unital C*-algebra are studied. The largest of these subsets has a natural interpretation as the space of invariant means. II₁-factor representations of a class of C*-algebras considered by Sorin Popa are also studied. These algebras are shown to have an unexpected variety of II₁-factor representations. This general theory is related to various other problems as well. Applications include: (1) A characterization of R^ω-embeddable factors in terms of Lance's WEP. (2) A classification theorem for certain simple, nuclear C*-algebras with unique trace. (3) For a self-adjoint operator there always exists a filtration such that the finite section method (from numerical analysis) works as well as could be hoped for. (4) New examples of non-tracially AF algebras which answer negatively questions of Sorin Popa and Huaxin Lin.

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• Tracial invariants, classification and II₁ factor representations of Popa algebras
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